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# A citrus fruit grower receives $15 for each crate of oranges  post reply Question banks Downloads My Bookmarks Reviews Important topics Author Message TAGS: ### Hide Tags Math Expert Joined: 02 Sep 2009 Posts: 41891 Kudos [?]: 129094 [0], given: 12194 Re: Gmat prep2 [#permalink] ### Show Tags 21 Apr 2012, 10:45 catty2004 wrote: Bunuel wrote: Joanna bought only$0.15 stamps and $0.29 stamps. How many$0.15 stamps did she buy?

Let $$x$$ be the # of $0.15 stamps and $$y$$ the # of$0.29 stamps. Note that $$x$$ and $$y$$ must be an integers. Q: $$x=?$$

(1) She bought $4.40 worth of stamps --> $$15x+29y=440$$. Only one integer combination of $$x$$ and $$y$$ is possible to satisfy $$15x+29y=440$$: $$x=10$$ and $$y=10$$. Sufficient. (2) She bought an equal number of$0.15 stamps and $0.29 stamps --> $$x=y$$. Not sufficient. Answer: A. So when we have equation of a type $$ax+by=c$$ and we know that x and y are integers, there can be multiple solutions possible for x and y (eg $$5x+6y=12900$$) OR just one combination (eg $$15x+29y=440$$). Hence in some cases $$ax+by=c$$ is NOT sufficient and in some cases it's sufficient. Hope it helps. How can one identify one or multiple solution for $$ax+by=c$$? (i.e. how did you arrive at the conclusion that only one integer combo satisfy $$15x+29y=440$$? Trial and error plus some logic and knowledge of basics of number properties should help you to identify this. For more on this type of questions check: eunice-sold-several-cakes-if-each-cake-sold-for-either-109602.html martha-bought-several-pencils-if-each-pencil-was-either-a-100204.html a-rental-car-agency-purchases-fleet-vehicles-in-two-sizes-a-105682.html joe-bought-only-twenty-cent-stamps-and-thirty-cent-stamps-106212.html a-certain-fruit-stand-sold-apples-for-0-70-each-and-bananas-101966.html joanna-bought-only-0-15-stamps-and-0-29-stamps-how-many-101743.html Hope it helps. _________________ Kudos [?]: 129094 [0], given: 12194 Manager Joined: 09 Apr 2012 Posts: 63 Kudos [?]: 67 [0], given: 29 Re: A citrus fruit grower receives$15 for each crate of oranges [#permalink]

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12 Oct 2012, 21:20
Mixing trial and error with number properties would save you some time.

(In relation to the question with 0.15 and 0.29 stamps).

The option says 0.15x+0.29y=4.40.

15x+29y=440; 15x=440-29y...
so y has to be a multiple of 5.

at most y can be 5 or 10.(y=15 or greater would yield a negative number)
y=5 doesnot give you a solution. y=10 is the only solution. From this X can be calculated.
SUFFICIENT

11x +28y=440 Sufficient.
11x+20y=440 Sufficient.
11x +18y Not sufficient. (11x=440-18y. assuming y=11z, x=40-18z. so x could be 22 or 4).

Kudos [?]: 67 [0], given: 29